<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html><head><title>R: Michelson's Determinations of the Velocity of Light</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link rel="stylesheet" type="text/css" href="R.css">
</head><body>

<table width="100%" summary="page for Michelson"><tr><td>Michelson</td><td align="right">R Documentation</td></tr></table>

<h2>
Michelson's Determinations of the Velocity of Light
</h2>

<h3>Description</h3>


<p>The data frame <code>Michelson</code> gives Albert Michelson's measurements of the velocity of light in air, 
made from June 5 to July 2, 1879, reported in Michelson (1882). 
The given values + 299,000 are Michelson's measurements in km/sec. 
The number of cases is 100 and the &quot;true&quot; value on this scale is 734.5.
</p>
<p>Stigler (1977) used these data to illustrate properties of robust estimators
with real, historical data.  For this purpose, he divided the 100 measurements
into 5 sets of 20 each.  These are contained in  <code>MichelsonSets</code>.
</p>


<h3>Usage</h3>

<pre>
data(Michelson)
data(MichelsonSets)
</pre>


<h3>Format</h3>


<p><code>Michelson</code>: A data frame with 100 observations on the following variable, given in time order of
data collection
</p>

<dl>
<dt><code>velocity</code></dt><dd><p>a numeric vector</p>
</dd>
</dl>

<p><code>MichelsonSets</code>: A 20 x 5 matrix, with format 
int [1:20, 1:5] 850 850 1000 810 960 800 830 830 880 720 ...
- attr(*, &quot;dimnames&quot;)=List of 2
..$ : NULL
..$ : chr [1:5] &quot;ds12&quot; &quot;ds13&quot; &quot;ds14&quot; &quot;ds15&quot; ...
</p>


<h3>Details</h3>


<p>The &quot;true&quot; value is taken to be 734.5, arrived at by taking the &quot;true&quot; speed of light
in a vacuum to be 299,792.5 km/sec, and adjusting for the velocity in air.
</p>
<p>The data values are recorded in order, and so may also be taken as a time series.
</p>


<h3>Source</h3>


<p>Kyle Siegrist, &quot;Virtual Laboratories in Probability and Statistics&quot;, <a href="http://www.math.uah.edu/stat/data/Michelson.xhtml">http://www.math.uah.edu/stat/data/Michelson.xhtml</a>
</p>
<p>Stephen M. Stigler (1977), &quot;Do robust estimators work with <EM>real</EM> data?&quot;, <EM>Annals of Statistics</EM>,  5, 1055-1098
</p>


<h3>References</h3>


<p>Michelson, A. A. (1882). &quot;Experimental determination of the velocity of light made at the
United States Naval Academy, Anapolis&quot;. <EM>Astronomical Papers</EM>, 1,109-145,
U. S. Nautical Almanac Office.
</p>


<h3>See Also</h3>


<p><code>morley</code> for these data in another format
</p>


<h3>Examples</h3>

<pre>
data(Michelson)

# density plot (default bandwidth &amp; 0.6 * bw)
plot(density(Michelson$velocity), xlab="Speed of light - 299000 (km/s)",
	main="Density plots of Michelson data")
lines(density(Michelson$velocity, adjust=0.6), lty=2)
rug(jitter(Michelson$velocity))
abline(v=mean(Michelson$velocity), col="blue")
abline(v=734.5, col="red", lwd=2)
text(mean(Michelson$velocity), .004, "mean", srt=90, pos=2)
text(734.5, .004, "true", srt=90, pos=2)

# index / time series plot
plot(Michelson$velocity, type="b")
abline(h=734.5, col="red", lwd=2)
lines(lowess(Michelson$velocity), col="blue", lwd=2)

# examine lag=1 differences
plot(diff(Michelson$velocity), type="b")
lines(lowess(diff(Michelson$velocity)), col="blue", lwd=2)

# examine different data sets
boxplot(MichelsonSets, ylab="Velocity of light - 299000 (km/s)", xlab="Data set")
abline(h=734.5, col="red", lwd=2)

# means and trimmed means
(mn &lt;-apply(MichelsonSets, 2, mean))
(tm &lt;- apply(MichelsonSets, 2, mean, trim=.1))
points(1:5, mn)
points(1:5+.05, tm, pch=16, col="blue")

</pre>


</body></html>
